Contribution and Reservation

10²⁴⁴+3 =: 1(0)₂₄₃3_<245>; = 7² · [204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367347_<243>] RESERVED

Status

Expression:	10²⁴⁴+3
Composite Factor:	204081632653061224489795918367346938775510204081632653061224 489795918367346938775510204081632653061224489795918367346938 775510204081632653061224489795918367346938775510204081632653 061224489795918367346938775510204081632653061224489795918367 347 (243-digit)
Status:	Not factored. Reserved by Lionel Debroux for submitting in the future.

How to factor it

ECM, P-1, P+1

Look for prime factors by GMP-ECM first. Refer to the section "Efforts by ECM". Not only ECM but also P-1/P+1 may be helpful.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 244.00-digit and the GNFS difficulty is 242.31-digit. SNFS must be faster than GNFS. It will take about 566 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 10003_244.
Put the following polynomial file 10003_244.poly in there too.
And then, run "perl factMsieve.pl 10003_244".

10003_244.poly

n: 204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367347
m: 10000000000000000000000000000000000000000
deg: 6
c6: 10000
c0: 3
skew: 0.26
type: snfs
lss: 1
rlim: 82000000
alim: 82000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
rlambda: 2.7
alambda: 2.7

These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 243-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)	Name
45	11e6	20	Serge Batalov	Dec 16, 2008
		580	Serge Batalov	Jan 2, 2009
		1420	Serge Batalov	Jan 3, 2009
		2020 / 912
50	43e6	1000	yoyo@home	Jan 15, 2010
		1000 / 7090
		/ 6090
55	11e7	0 / 17284 (2526)
55	11e7	/ 17284 (2526)
60	26e7	0 / 41868 (7435)
60	26e7	/ 41868 (7435)
65	85e7	0 / 69379 (13563)
65	85e7	/ 69379 (13563)

Command line to find prime factors up to about 50-digit

echo 204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367347 | ecm -n -c 6090 43e6

Command line to find prime factors up to about 55-digit

echo 204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367347 | ecm -n -c 17284 11e7

Command line to find prime factors up to about 60-digit

echo 204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367347 | ecm -n -c 41868 26e7

Command line to find prime factors up to about 65-digit

echo 204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367347 | ecm -n -c 69379 85e7

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